{"version":1,"lectureId":"01M14TXV617E4GZ23JQR30YYCA","attempt":0,"publication":{"slug":"monopoly-marginal-revenue-and-price-discrimination","title":"Monopoly, Marginal Revenue, and Price Discrimination","subject":"economics","summary":"Why monopoly pricing is constrained by market demand, why marginal revenue lies below price, and why it falls twice as fast under linear demand. The lecture derives the monopoly quantity and price, compares monopoly with competition through surplus and deadweight loss, then examines third-degree and perfect price discrimination with explicit attention to restored trades, efficiency, profit, and who captures the value created.","metaDescription":"Derive monopoly marginal revenue, compare monopoly with competition, and trace welfare under group and perfect price discrimination.","transcript":"A monopolist is the only seller, but that does not make demand disappear. Buyers still decide how many units they will purchase at each price. The firm may choose a point on market demand, not a price and quantity independently. Here is a market demand curve. Quantity runs across the bottom, price runs up the side, and the downward slope says that reaching more buyers requires a lower price. At quantity twenty, demand allows a price of sixty. The point twenty, sixty is therefore one feasible price-quantity choice, and the rectangle beneath it is the firm's total revenue. Read that choice algebraically. Demand gives sixty dollars per unit, and twenty units at sixty dollars produce total revenue of twelve hundred dollars. Now ask the firm to sell one additional unit. Demand says quantity twenty-one can be sold only if the market price falls from sixty to fifty-eight. The extra unit brings in fifty-eight dollars. That is the narrow green strip. But the firm must also cut the price by two dollars on each of the twenty units it was already selling. The red band is that lost revenue: twenty earlier units times a two-dollar reduction, or forty dollars lost. Marginal revenue is the green gain minus the red loss, not simply the new unit's price. Fifty-eight gained minus forty lost leaves only eighteen dollars of additional revenue. The new unit sells for fifty-eight, yet its marginal revenue is eighteen. That gap between price and marginal revenue is the central monopoly constraint. Expanding sales earns revenue on the new unit, but lowering one market price sacrifices revenue on every earlier unit. The same logic can be written for every quantity on a linear demand curve. Let inverse demand be price equals a minus b Q. The intercept a is the price of the first infinitesimal unit. The coefficient b records how quickly the market price must fall as total output rises. Total revenue is price times quantity. Substitute demand into that product, then multiply out. Revenue is a Q minus b Q squared. Differentiate revenue with respect to quantity. The derivative of a Q is a, while the derivative of minus b Q squared is minus two b Q. So marginal revenue has the same vertical intercept a as demand, but its slope is minus two b instead of minus b. It falls twice as fast because the price reduction applies to the old units as well as the new one. For our numerical demand, price is one hundred minus two Q. Marginal revenue is one hundred minus four Q. Draw the red marginal-revenue curve. Both curves begin at one hundred. Demand reaches the quantity axis at fifty, while marginal revenue reaches it halfway across, at twenty-five. The algebra and the graph tell the same story. Linear demand falls by two dollars per additional unit; marginal revenue falls by four because it includes both the new sale and the price cut imposed on existing sales. Now turn marginal revenue into a quantity decision. We will keep one posted price, constant marginal cost of twenty, and no fixed cost. Those assumptions make the allocation and the welfare accounting transparent. The blue curve is demand, the red curve is marginal revenue, and the green line is marginal cost. Demand describes buyers. Marginal revenue and marginal cost describe the consequence of producing one more unit. At quantity ten, marginal revenue exceeds marginal cost. Another unit adds more to revenue than to cost, so stopping there would leave profitable units unproduced. Push output to twenty-five. Marginal revenue has fallen below marginal cost, so the last units destroy profit. Move back until the red and green readings meet, at quantity twenty. The interior profit maximum therefore satisfies marginal revenue equal to marginal cost. Substitute the numerical curves: one hundred minus four Q equals twenty. Solving gives the monopoly quantity, twenty. Notice what has been chosen so far: quantity, not price. To find the price, move vertically from quantity twenty to the demand curve. Demand says buyers will pay sixty for each of those twenty units. This order matters. Marginal revenue equal to marginal cost selects quantity. Demand then supplies the single market price. Reading price from marginal revenue would confuse an incremental revenue with what buyers actually pay. For the competitive benchmark, price equals marginal cost. Demand reaches twenty dollars at quantity forty, so competition produces forty units at a price of twenty. Place the two outcomes beside the same market. Monopoly stops at twenty and charges sixty. Competition continues to forty and charges twenty. Under monopoly, the yellow triangle is consumer surplus. Buyers receive the difference between willingness to pay and the sixty-dollar price on the twenty units sold. The magenta rectangle is producer surplus. With constant marginal cost twenty and price sixty, the firm receives forty dollars of surplus on each of twenty units, for eight hundred. The red triangle contains quantities twenty through forty. For every unit there, willingness to pay exceeds marginal cost, yet the monopolist does not sell it because expansion would force down the price on earlier units. Those are mutually beneficial trades that never occur. Their lost total surplus is deadweight loss, four hundred. Monopoly total surplus is twelve hundred. Switch to competition. Output reaches forty, the point where willingness to pay just equals marginal cost. The formerly missing trades now occur. With price equal to constant marginal cost and no fixed cost, consumer surplus is sixteen hundred and producer surplus is zero. Total surplus is sixteen hundred, and deadweight loss is zero. The competitive benchmark maximizes total surplus because every unit worth at least its cost is produced. The monopoly restriction lowers quantity from forty to twenty and destroys four hundred of that possible value. Two questions must remain separate. Efficiency asks how much total value is created. Distribution asks whether buyers or the firm capture that value. Monopoly changes both, but the missing red triangle is a loss to everyone, not a transfer between them. Now suppose the seller can separate customers into two observable groups. Group A has stronger demand than group B. The product and marginal cost are the same, but willingness to pay differs. This possibility requires strong assumptions. The firm must identify each group, keep customers from pretending to belong to the other group, and prevent low-price buyers from reselling to high-price buyers. The blue curve is demand in group A: price equals one hundred minus Q A. The yellow curve is demand in group B: price equals forty minus Q B. The green marginal-cost line is twenty in both markets. Before allowing separate prices, force the firm to post one common price. That benchmark will show exactly which trades discrimination restores. At prices of forty or more, group B buys nothing. Only group A remains, with quantity one hundred minus price. Profit is price minus marginal cost, times group A quantity. Differentiate with respect to price. The high-price region has its maximum at a common price of sixty. At sixty, group A buys forty units, group B buys none, and profit is sixteen hundred. The gray line and point mark this one-price outcome. Could a lower common price that serves both groups do better? Below forty, total quantity is one hundred forty minus two P. Its unconstrained optimum would lie above the permitted range, so the best feasible point in that region is the boundary price forty. At that boundary profit is only twelve hundred, below sixteen hundred. Therefore the best uniform price is sixty, even though it excludes every buyer in group B. Now allow a separate price in each group. The firm treats each market's marginal revenue independently, while comparing both with the same marginal cost. In group A, marginal revenue equals twenty at quantity forty. Demand then gives price sixty, exactly the outcome group A already had. In group B, marginal revenue equals twenty at quantity ten. Demand gives a group-B price of thirty, low enough to create ten sales that the uniform price had excluded. Total output rises from forty to fifty, and profit rises from sixteen hundred to seventeen hundred. In this example, segmentation restores trades rather than merely reallocating a fixed total. Now separate efficiency from distribution. Under one price, forty units are sold, consumer surplus is eight hundred, producer surplus is sixteen hundred, and total surplus is twenty-four hundred. The one-price deadweight loss is one thousand. Eight hundred comes from missing group-A trades beyond quantity forty, and two hundred comes from excluding the entire efficient range in group B. With two prices, group A remains at forty units while group B gains ten. Total quantity becomes fifty. The restored group-B trades create one hundred fifty dollars of surplus. Fifty goes to group-B consumers as the yellow triangle, and one hundred goes to the firm as the magenta rectangle. Consumer surplus across both groups rises to eight hundred fifty, producer surplus rises to seventeen hundred, and total surplus rises to twenty-five hundred fifty. Deadweight loss falls from one thousand to eight hundred fifty. It does not disappear: group A still stops at forty, and group B still stops at ten instead of the efficient quantity twenty. This welfare improvement is an example, not a universal theorem. Third-degree discrimination can raise or lower total output, and it can redirect units toward groups with higher or lower willingness to pay. What is reliable is the firm's incentive: if separation is voluntary and feasible, its profit rises. What happens to total surplus depends on which trades appear, which disappear, and how production is reallocated. Who captures the gains is a further question, distinct from whether gains exist at all. Perfect, or first-degree, price discrimination is a much stronger benchmark. The firm knows each buyer's exact willingness to pay and can charge that amount unit by unit. It must also prevent resale. Otherwise a buyer offered a low price could resell to someone facing a high price, and the entire pricing scheme would unravel. The blue demand curve now has a second interpretation. Its height at each quantity is the willingness to pay for that marginal unit. The green line remains marginal cost twenty. Begin near the left. The fifth unit is worth ninety dollars to its buyer. Under perfect discrimination, the firm can charge ninety for that unit without lowering the prices paid for the units before it. That last clause removes the price-cut loss that pushed marginal revenue below demand under one-price monopoly. Each unit contributes its own willingness to pay, less its own production cost. Move to unit twenty. Its willingness to pay is sixty. Earlier buyers may still pay more than sixty because their individual prices do not have to match this buyer's price. Move farther, to unit thirty-five. That buyer is willing to pay thirty, still ten dollars above marginal cost, so producing the unit creates ten dollars of total surplus. Approach unit forty. At unit forty, willingness to pay is twenty, exactly marginal cost. Beyond forty, willingness to pay would be below cost, so those units should not be produced. The rule is now different from one-price monopoly. Revenue from the marginal unit equals that unit's own demand price because selling it does not reduce the prices charged on earlier units. Produce while willingness to pay is at least marginal cost. For our market, set one hundred minus two Q equal to twenty. The result is quantity forty, the same efficient quantity produced under competition. Perfect discrimination restores every trade whose value covers its cost. Efficiency has returned, but competitive pricing has not. There is no one price here. Early units carry high prices, later units carry lower prices, and the final unit is priced at marginal cost. Return briefly to the one-price monopoly. It sold twenty units at sixty. The yellow triangle was consumer surplus, the magenta rectangle was producer surplus, and the red triangle was deadweight loss. Under perfect discrimination, output extends from twenty to forty. The missing red trades return, so deadweight loss falls from four hundred to zero. But each buyer is charged exactly what the unit is worth to that buyer. The difference between willingness to pay and marginal cost is therefore captured by the firm, not left with consumers. Producer surplus becomes the entire magenta triangle, sixteen hundred. Consumer surplus is zero because every buyer pays their full willingness to pay. Total surplus is also sixteen hundred, the same efficient total as under competition. The firm has not created extra value beyond the efficient allocation. It has changed who receives that value. That completes the distinction. A one-price monopolist restricts quantity because expanding sales lowers the price on earlier units. Third-degree discrimination may restore some trades by separating groups. Perfect discrimination restores every efficient trade, eliminates deadweight loss, and transfers the available surplus to the monopolist.","watch":{"version":1,"scenes":[{"title":"One More Unit Changes Every Price","start":0,"end":210.46554166666664,"objects":{"demand_curve":"a FunctionPlot [blue] labelled \"D\" drawn in plot (function=<function>, x_range=(0.0, 50.0))","heading_linear":"a Heading that says \"Why Marginal Revenue Falls Twice as Fast\"","linear_work":"a Derivation [text] that says \"$P(Q) &= a-b Q \\ R(Q) &= P(Q) Q \\ &=(a-b Q) Q \\ &=a Q-b Q^2 \\ upright(\"MR\")(Q) &= frac(dif R, dif Q)=a-2 b Q$\"","lost_revenue":"a Polygon [red] drawn in plot (vertices=((0.0, 58.0), (20.0, 58.0), (20.0, 60.0), (0.0, 60.0)), fill_opacity=0.55)","mr_curve":"a FunctionPlot [red] labelled \"upright(\"MR\")\" drawn in plot (function=<function>, x_range=(0.0, 25.0))","net_change":"a Math [text] that says \"$Delta R=18$\"","new_price":"a Math [text] that says \"$P(21)=100-2(21)=58$\"","new_unit_revenue":"a Polygon [green] drawn in plot (vertices=((20.0, 0.0), (21.0, 0.0), (21.0, 58.0), (20.0, 58.0)), fill_opacity=0.58)","numeric_demand":"a Math [text] that says \"$P(Q)=100-2Q$\"","numeric_mr":"a Math [text] that says \"$upright(\"MR\")(Q)=100-4Q$\"","old_price":"a Math [text] that says \"$P(20)=100-2(20)=60$\"","old_revenue":"a Polygon [blue] drawn in plot (vertices=((0.0, 0.0), (20.0, 0.0), (20.0, 60.0), (0.0, 60.0)), fill_opacity=0.18)","old_total":"a Math [text] that says \"$R(20)=20(60)=1200$\"","plot":"an Axes (x_range=(0.0, 52.0), y_range=(0.0, 110.0), x_ticks_every=5.0)","point":"a Point [yellow] drawn in plot (location=(0.0, 100.0))","point_2":"a Point [yellow] drawn in plot (location=(50.0, 0.0))","point_3":"a Point [yellow] drawn in plot (location=(25.0, 0.0))","q20":"a PlotPoint [yellow] labelled \"(20,60)\" drawn in plot (target='demand_curve', x=20.0)","q21":"a PlotPoint [green] labelled \"(21,58)\" drawn in plot (target='demand_curve', x=21.0)","question":"a Panel that says \"If a monopolist faces the whole market demand curve, why can it not simply choose any high price it likes?\"","revenue_change":"a Math [text] that says \"$Delta R=58-20(2)$\"","slope_result":"a Math [text] that says \"$upright(\"same intercept\"), quad upright(\"twice the slope\")$\""},"beats":[{"start":0,"say":"A monopolist is the only seller, but that does not make demand disappear. Buyers still decide how many units they will purchase at each price. The firm may choose a point on market demand, not a price and quantity independently.","live":[],"does":[[0,"question is shown on the screen, written out."]]},{"start":14.59,"say":"Here is a market demand curve. Quantity runs across the bottom, price runs up the side, and the downward slope says that reaching more buyers requires a lower price.","live":["question"],"does":[[16.354999999999997,"plot is shown on the screen, written out."],[16.354999999999997,"demand_curve is shown on the screen, drawn."]]},{"start":26.835,"say":"At quantity twenty, demand allows a price of sixty. The point twenty, sixty is therefore one feasible price-quantity choice, and the rectangle beneath it is the firm's total revenue.","live":["plot","question","demand_curve"],"does":[[27.855999999999998,"q20 is shown on the screen, written out."],[36.239000000000004,"old_revenue is shown on the screen, written out."]]},{"start":40.55,"say":"Read that choice algebraically. Demand gives sixty dollars per unit, and twenty units at sixty dollars produce total revenue of twelve hundred dollars.","live":["plot","question","demand_curve","q20","old_revenue"],"does":[[43.847,"plot moves to a new place on the board."],[43.847,"old_price is shown on the screen, written out."],[48.735,"old_total is shown on the screen, written out."]]},{"start":50.902,"say":"Now ask the firm to sell one additional unit. Demand says quantity twenty-one can be sold only if the market price falls from sixty to fifty-eight.","live":["plot","question","demand_curve","q20","old_revenue","old_price","old_total"],"does":[[56.173,"q21 is shown on the screen, written out."],[60.028000000000006,"new_price is shown on the screen, written out."]]},{"start":61.626000000000005,"say":"The extra unit brings in fifty-eight dollars. That is the narrow green strip. But the firm must also cut the price by two dollars on each of the twenty units it was already selling.","live":["plot","question","demand_curve","q20","old_revenue","old_price","old_total","new_price","q21"],"does":[[65.887,"new_unit_revenue is shown on the screen, written out."],[68.30199999999999,"lost_revenue is shown on the screen, written out."]]},{"start":73.0235,"say":"The red band is that lost revenue: twenty earlier units times a two-dollar reduction, or forty dollars lost. Marginal revenue is the green gain minus the red loss, not simply the new unit's price.","live":["plot","question","demand_curve","q20","old_revenue","old_price","old_total","new_price","q21","new_unit_revenue","lost_revenue"],"does":[[74.47500000000001,"revenue_change is shown on the screen, written out."],[82.706,"revenue_change (the \"58\" part) is emphasized."],[84.06400000000001,"revenue_change (the \"20(2)\" part) is emphasized."],[84.06400000000001,"revenue_change (the \"58\" part) is no longer emphasized."],[87.0945,"revenue_change (the \"20(2)\" part) is no longer emphasized."]]},{"start":87.6945,"say":"Fifty-eight gained minus forty lost leaves only eighteen dollars of additional revenue. The new unit sells for fifty-eight, yet its marginal revenue is eighteen.","live":["plot","question","demand_curve","q20","old_revenue","old_price","old_total","new_price","revenue_change","q21","new_unit_revenue","lost_revenue"],"does":[[91.06100000000002,"net_change is shown on the screen, written out."],[98.4105,"A box is drawn around net_change."]]},{"start":99.01050000000001,"say":"That gap between price and marginal revenue is the central monopoly constraint. Expanding sales earns revenue on the new unit, but lowering one market price sacrifices revenue on every earlier unit.","live":["plot","question","demand_curve","q20","old_revenue","old_price","old_total","new_price","revenue_change","net_change","q21","new_unit_revenue","lost_revenue"],"does":[[106.72000000000001,"new_unit_revenue is indicated — a transient flash."],[111.36400000000002,"lost_revenue is indicated — a transient flash."]]},{"start":113.7825,"say":"The same logic can be written for every quantity on a linear demand curve. Let inverse demand be price equals a minus b Q.","live":null,"does":[[113.7825,"old_revenue is hidden from the screen."],[113.7825,"lost_revenue is hidden from the screen."],[113.7825,"new_unit_revenue is hidden from the screen."],[113.7825,"q20 is hidden from the screen."],[113.7825,"q21 is hidden from the screen."],[122.8845,"plot moves to a new place on the board."],[122.8845,"net_change is hidden from the screen — left the board."],[122.8845,"new_price is hidden from the screen — left the board."],[122.8845,"old_price is hidden from the screen — left the board."],[122.8845,"old_total is hidden from the screen — left the board."],[122.8845,"question is hidden from the screen — left the board."],[122.8845,"revenue_change is hidden from the screen — left the board."]]},{"start":123.4845,"say":"The intercept a is the price of the first infinitesimal unit. The coefficient b records how quickly the market price must fall as total output rises.","live":["plot","demand_curve"],"does":[[123.4845,"heading_linear is shown on the screen, written out."],[125.13400000000001,"linear_work is shown on the screen, written out."]]},{"start":134.1155,"say":"Total revenue is price times quantity. Substitute demand into that product, then multiply out. Revenue is a Q minus b Q squared.","live":["plot","demand_curve","heading_linear"],"does":[[134.464,"linear_work is shown on the screen, written out."],[137.738,"linear_work is shown on the screen, written out."],[140.35000000000002,"linear_work is shown on the screen, written out."]]},{"start":145.989,"say":"Differentiate revenue with respect to quantity. The derivative of a Q is a, while the derivative of minus b Q squared is minus two b Q.","live":null,"does":[[146.33700000000002,"linear_work is shown on the screen, written out."]]},{"start":158.0015,"say":"So marginal revenue has the same vertical intercept a as demand, but its slope is minus two b instead of minus b. It falls twice as fast because the price reduction applies to the old units as well as the new one.","live":null,"does":[[160.23100000000002,"linear_work (the \"a\" part) is emphasized."],[160.23100000000002,"linear_work (the \"a\" part) is emphasized."],[163.28400000000002,"linear_work (the \"a\" part) is no longer emphasized."],[163.28400000000002,"linear_work (the \"a\" part) is no longer emphasized."],[167.46400000000003,"linear_work (the \"2 b Q\" part) is emphasized."],[172.677,"linear_work (the \"2 b Q\" part) is no longer emphasized."]]},{"start":173.277,"say":"For our numerical demand, price is one hundred minus two Q. Marginal revenue is one hundred minus four Q.","live":null,"does":[[175.48300000000003,"numeric_demand is shown on the screen, written out."],[178.37400000000002,"numeric_mr is shown on the screen, written out."]]},{"start":181.98049999999998,"say":"Draw the red marginal-revenue curve. Both curves begin at one hundred. Demand reaches the quantity axis at fifty, while marginal revenue reaches it halfway across, at twenty-five.","live":["plot","demand_curve","numeric_demand","numeric_mr","heading_linear"],"does":[[182.74700000000004,"mr_curve is shown on the screen, drawn."],[186.46200000000005,"point is shown on the screen, grown."],[188.46200000000005,"point is hidden from the screen."],[189.65500000000003,"point_2 is shown on the screen, grown."],[191.65500000000003,"point_2 is hidden from the screen."],[193.48600000000005,"point_3 is shown on the screen, grown."]]},{"start":195.28199999999998,"say":"The algebra and the graph tell the same story. Linear demand falls by two dollars per additional unit; marginal revenue falls by four because it includes both the new sale and the price cut imposed on existing sales.","live":["plot","demand_curve","numeric_demand","numeric_mr","heading_linear","mr_curve","point_3"],"does":[[195.48600000000005,"point_3 is hidden from the screen."],[197.26700000000002,"slope_result is shown on the screen, written out."],[200.09900000000002,"numeric_demand (the \"2Q\" part) is emphasized."],[203.89600000000002,"numeric_mr (the \"4Q\" part) is emphasized."],[209.17387499999998,"numeric_demand (the \"2Q\" part) is no longer emphasized."],[209.17387499999998,"numeric_mr (the \"4Q\" part) is no longer emphasized."],[209.42387499999998,"heading_linear is hidden from the screen — left the board."],[209.42387499999998,"linear_work is hidden from the screen — left the board."],[209.42387499999998,"numeric_demand is hidden from the screen — left the board."],[209.42387499999998,"numeric_mr is hidden from the screen — left the board."],[209.42387499999998,"plot is hidden from the screen — left the board."],[209.42387499999998,"demand_curve is hidden from the screen — plot left the board."],[209.42387499999998,"mr_curve is hidden from the screen — plot left the board."],[209.42387499999998,"slope_result is hidden from the screen — left the board."]]}]},{"title":"The Monopoly Choice and the Missing Trades","start":210.46554166666664,"end":440.94006249999995,"objects":{"assumptions":"a Panel that says \"One firm serves the whole market, posts one price, faces known demand, and has constant marginal cost of 20. 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We will keep one posted price, constant marginal cost of twenty, and no fixed cost. Those assumptions make the allocation and the welfare accounting transparent.","live":[],"does":[[210.46554166666664,"heading_choice is shown on the screen, written out."],[221.16954166666665,"assumptions is shown on the screen, written out."]]},{"start":225.78704166666665,"say":"The blue curve is demand, the red curve is marginal revenue, and the green line is marginal cost. Demand describes buyers. Marginal revenue and marginal cost describe the consequence of producing one more unit.","live":["assumptions","heading_choice"],"does":[[226.32054166666663,"plot is shown on the screen, written out."],[226.32054166666663,"demand_curve is shown on the screen, drawn."],[228.16654166666663,"mr_curve is shown on the screen, drawn."],[230.48854166666663,"mc_curve is shown on the screen, drawn."]]},{"start":241.18954166666663,"say":"At quantity ten, marginal revenue exceeds marginal cost. Another unit adds more to revenue than to cost, so stopping there would leave profitable units unproduced.","live":["assumptions","plot","heading_choice","demand_curve","mr_curve","mc_curve"],"does":[[241.75854166666664,"mr_probe is shown on the screen, written out."],[241.75854166666664,"mc_probe is shown on the screen, written out."]]},{"start":252.83104166666664,"say":"Push output to twenty-five. Marginal revenue has fallen below marginal cost, so the last units destroy profit. Move back until the red and green readings meet, at quantity twenty.","live":["assumptions","plot","heading_choice","demand_curve","mr_curve","mc_curve","mr_probe","mc_probe"],"does":[[254.02654166666665,"mr_probe is redrawn as the numbers it depends on change."],[254.02654166666665,"mc_probe is redrawn as the numbers it depends on change."],[254.02654166666665,"trial ticks to 25.0."],[263.47754166666664,"mr_probe is redrawn as the numbers it depends on change."],[263.47754166666664,"mc_probe is redrawn as the numbers it depends on change."],[263.47754166666664,"trial ticks to 20.0."]]},{"start":266.5815416666666,"say":"The interior profit maximum therefore satisfies marginal revenue equal to marginal cost. Substitute the numerical curves: one hundred minus four Q equals twenty.","live":null,"does":[[266.5815416666666,"plot moves to a new place on the board."],[266.5815416666666,"assumptions is hidden from the screen — left the board."],[266.5815416666666,"mr_probe is hidden from the screen."],[266.5815416666666,"mc_probe is hidden from the screen."],[266.5815416666666,"optimization is shown on the screen, written out."],[273.95354166666664,"optimization is shown on the screen, written out."]]},{"start":279.09304166666664,"say":"Solving gives the monopoly quantity, twenty. Notice what has been chosen so far: quantity, not price.","live":["plot","heading_choice","demand_curve","mr_curve","mc_curve"],"does":[[281.38054166666666,"optimization is shown on the screen, written out."]]},{"start":287.1465416666666,"say":"To find the price, move vertically from quantity twenty to the demand curve. Demand says buyers will pay sixty for each of those twenty units.","live":null,"does":[[288.77254166666665,"monopoly_quantity is shown on the screen, written out."],[290.66454166666665,"monopoly_point is shown on the screen, written out."],[293.85754166666663,"optimization is shown on the screen, written out."]]},{"start":296.86104166666667,"say":"This order matters. Marginal revenue equal to marginal cost selects quantity. Demand then supplies the single market price. Reading price from marginal revenue would confuse an incremental revenue with what buyers actually pay.","live":["plot","heading_choice","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point"],"does":[[302.23654166666665,"optimization (the \"Q_M\" part) is emphasized."],[303.6755416666666,"optimization (the \"Q_M\" part) is no longer emphasized."],[305.7425416666666,"optimization (the \"P_M\" part) is emphasized."],[313.47504166666664,"optimization (the \"P_M\" part) is no longer emphasized."]]},{"start":314.0750416666666,"say":"For the competitive benchmark, price equals marginal cost. Demand reaches twenty dollars at quantity forty, so competition produces forty units at a price of twenty.","live":null,"does":[[314.9455416666666,"optimization is shown on the screen, written out."],[320.03054166666664,"competitive_quantity is shown on the screen, written out."],[320.03054166666664,"competitive_point is shown on the screen, written out."],[324.81404166666664,"plot moves to a new place on the board."],[324.81404166666664,"heading_choice is hidden from the screen — left the board."],[324.81404166666664,"optimization is hidden from the screen — left the board."]]},{"start":326.0140416666666,"say":"Place the two outcomes beside the same market. Monopoly stops at twenty and charges sixty. Competition continues to forty and charges twenty.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point"],"does":[[326.0140416666666,"heading_welfare is shown on the screen, written out."],[329.4735416666666,"monopoly_label is shown on the screen, written out."],[330.6235416666666,"monopoly_result is shown on the screen, written out."],[332.4695416666666,"competition_label is shown on the screen, written out."],[333.73454166666664,"competition_result is shown on the screen, written out."]]},{"start":336.4590416666666,"say":"Under monopoly, the yellow triangle is consumer surplus. Buyers receive the difference between willingness to pay and the sixty-dollar price on the twenty units sold.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point","monopoly_label","monopoly_result","competition_label","competition_result","heading_welfare"],"does":[[337.8635416666666,"monopoly_cs is shown on the screen, written out."],[338.85054166666663,"monopoly_surplus is shown on the screen, written out."]]},{"start":347.2530416666666,"say":"The magenta rectangle is producer surplus. With constant marginal cost twenty and price sixty, the firm receives forty dollars of surplus on each of twenty units, for eight hundred.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point","monopoly_label","monopoly_result","monopoly_surplus","competition_label","competition_result","heading_welfare","monopoly_cs"],"does":[[347.7635416666666,"monopoly_ps is shown on the screen, written out."],[357.59754166666664,"monopoly_surplus (the \"upright(\"PS\")=800\" part) is emphasized."],[358.64304166666665,"monopoly_surplus (the \"upright(\"PS\")=800\" part) is no longer emphasized."]]},{"start":359.2430416666666,"say":"The red triangle contains quantities twenty through forty. For every unit there, willingness to pay exceeds marginal cost, yet the monopolist does not sell it because expansion would force down the price on earlier units.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point","monopoly_label","monopoly_result","monopoly_surplus","competition_label","competition_result","heading_welfare","monopoly_cs","monopoly_ps"],"does":[[359.79954166666664,"monopoly_dwl is shown on the screen, written out."],[361.73854166666666,"The segment (20.0, 0.0) to (40.0, 0.0) in plot is lit up."],[373.39504166666666,"plot: retire a lit segment (unemphasize_line)."]]},{"start":373.9950416666667,"say":"Those are mutually beneficial trades that never occur. Their lost total surplus is deadweight loss, four hundred. Monopoly total surplus is twelve hundred.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point","monopoly_label","monopoly_result","monopoly_surplus","competition_label","competition_result","heading_welfare","monopoly_cs","monopoly_ps","monopoly_dwl"],"does":[[379.4515416666667,"monopoly_total is shown on the screen, written out."],[380.45054166666665,"monopoly_dwl is indicated — a transient flash."]]},{"start":385.0670416666667,"say":"Switch to competition. Output reaches forty, the point where willingness to pay just equals marginal cost. The formerly missing trades now occur.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point","monopoly_label","monopoly_result","monopoly_surplus","monopoly_total","competition_label","competition_result","heading_welfare","monopoly_cs","monopoly_ps","monopoly_dwl"],"does":[[385.0670416666667,"monopoly_cs is hidden from the screen."],[385.0670416666667,"monopoly_ps is hidden from the screen."],[385.0670416666667,"monopoly_dwl is hidden from the screen."],[385.8795416666667,"competitive_cs is shown on the screen, written out."]]},{"start":395.90704166666666,"say":"With price equal to constant marginal cost and no fixed cost, consumer surplus is sixteen hundred and producer surplus is zero. Total surplus is sixteen hundred, and deadweight loss is zero.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point","monopoly_label","monopoly_result","monopoly_surplus","monopoly_total","competition_label","competition_result","heading_welfare","competitive_cs"],"does":[[399.8305416666667,"competition_surplus is shown on the screen, written out."],[404.4405416666667,"competition_total is shown on the screen, written out."]]},{"start":409.16154166666666,"say":"The competitive benchmark maximizes total surplus because every unit worth at least its cost is produced. The monopoly restriction lowers quantity from forty to twenty and destroys four hundred of that possible value.","live":["plot","demand_curve","mr_curve","mc_curve","monopoly_quantity","monopoly_point","competitive_quantity","competitive_point","monopoly_label","monopoly_result","monopoly_surplus","monopoly_total","competition_label","competition_result","competition_surplus","competition_total","heading_welfare","competitive_cs"],"does":[[411.3445416666667,"competition_total (the \"upright(\"TS\")=1600\" part) is emphasized."],[416.0575416666667,"competition_total (the \"upright(\"TS\")=1600\" part) is no longer emphasized."],[419.5525416666667,"monopoly_total (the \"upright(\"TS\")=1200\" part) is emphasized."],[422.22304166666663,"monopoly_total (the \"upright(\"TS\")=1200\" part) is no longer emphasized."]]},{"start":422.82304166666665,"say":"Two questions must remain separate. Efficiency asks how much total value is created. Distribution asks whether buyers or the firm capture that value. Monopoly changes both, but the missing red triangle is a loss to everyone, not a transfer between them.","live":null,"does":[[436.8485416666666,"monopoly_total (the \"upright(\"DWL\")=400\" part) is indicated — a transient flash."],[439.8983958333333,"competition_label is hidden from the screen — left the board."],[439.8983958333333,"competition_result is hidden from the screen — left the board."],[439.8983958333333,"competition_surplus is hidden from the screen — left the board."],[439.8983958333333,"competition_total is hidden from the screen — left the board."],[439.8983958333333,"heading_welfare is hidden from the screen — left the board."],[439.8983958333333,"monopoly_label is hidden from the screen — left the board."],[439.8983958333333,"monopoly_result is hidden from the screen — left the board."],[439.8983958333333,"monopoly_surplus is hidden from the screen — left the board."],[439.8983958333333,"monopoly_total is hidden from the screen — left the board."],[439.8983958333333,"plot is hidden from the screen — left the board."],[439.8983958333333,"demand_curve is hidden from the screen — plot left the board."],[439.8983958333333,"mr_curve is hidden from the screen — plot left the board."],[439.8983958333333,"mc_curve is hidden from the screen — plot left the board."],[439.8983958333333,"monopoly_quantity is hidden from the screen — plot left the board."],[439.8983958333333,"monopoly_point is hidden from the screen — plot left the board."],[439.8983958333333,"competitive_quantity is hidden from the screen — plot left the board."],[439.8983958333333,"competitive_point is hidden from the screen — plot left the board."],[439.8983958333333,"competitive_cs is hidden from the screen — plot left the board."]]}]},{"title":"Two Groups, Two Prices","start":440.94006249999995,"end":705.7370416666668,"objects":{"demand_curve_a":"a FunctionPlot [blue] labelled \"D_A\" drawn in market (function=<function>, x_range=(0.0, 85.0))","demand_curve_b":"a FunctionPlot [yellow] labelled \"D_B\" drawn in market (function=<function>, x_range=(0.0, 40.0))","heading_compare":"a Heading that says \"Which Trades Return, and Who Gains?\"","heading_groups":"a Heading that says \"Two Identifiable Customer Groups\"","heading_separate":"a Heading that says \"Then, Optimize Each Group Separately\"","heading_uniform":"a Heading that says \"First, One Price for Everyone\"","market":"an Axes (x_range=(0.0, 85.0), y_range=(0.0, 110.0), x_ticks_every=10.0)","mc_curve":"a FunctionPlot [green] labelled \"upright(\"MC\")\" drawn in market (function=<function>, x_range=(0.0, 85.0))","mr_curve_a":"a FunctionPlot [red] labelled \"upright(\"MR\")_A\" drawn in market (function=<function>, x_range=(0.0, 50.0))","mr_curve_b":"a FunctionPlot [magenta] labelled \"upright(\"MR\")_B\" drawn in market (function=<function>, x_range=(0.0, 20.0))","remaining_a_dwl":"a Polygon [red] drawn in market (vertices=((40.0, 20.0), (40.0, 60.0), (80.0, 20.0)), fill_opacity=0.24)","remaining_b_dwl":"a Polygon [red] drawn in market (vertices=((10.0, 20.0), (10.0, 30.0), (20.0, 20.0)), fill_opacity=0.45)","restored_b_cs":"a Polygon [yellow] drawn in market (vertices=((0.0, 30.0), (0.0, 40.0), (10.0, 30.0)), fill_opacity=0.38)","restored_b_ps":"a Polygon [magenta] drawn in market (vertices=((0.0, 20.0), (10.0, 20.0), (10.0, 30.0), (0.0, 30.0)), fill_opacity=0.34)","restriction":"a Panel that says \"The firm can identify each group, prevent resale, and charge a separate posted price in each market. Marginal cost is 20 for every unit.\"","separate_allocation":"a Math [text] that says \"$Q_A=40, quad Q_B=10, quad Q=50$\"","separate_b":"a PlotPoint [yellow] labelled \"T_B\" drawn in market (target='demand_curve_b', x=10.0)","separate_label":"a Tex [text] that says \"Two group prices\" (underline=True)","separate_total":"a Math [text] that says \"$upright(\"TS\")=2550, quad upright(\"DWL\")=850$\"","separate_welfare":"a Math [text] that says \"$upright(\"CS\")=850, quad upright(\"PS\")=1700$\"","separate_work":"a Derivation [text] that says \"$upright(\"MR\")_A &= upright(\"MC\") \\ 100-2Q_A &= 20 \\ Q_A=40, thin P_A &= 60 \\ upright(\"MR\")_B &= upright(\"MC\") \\ 40-2Q_B &= 20 \\ Q_B=10, thin P_B &= 30 \\ Q=50, thin pi &= 1700$\"","u0":"a Math [text] that says \"$P>=40: thin Q=100-P$\"","u1":"a Math [text] that says \"$pi=(P-20)(100-P)$\"","u2":"a Math [text] that says \"$pi'=120-2P=0$\"","u3":"a Math [text] that says \"$P_U=60 thin arrow.r thin pi=1600$\"","u4":"a Math [text] that says \"$Q_A=40, quad Q_B=0$\"","u5":"a Math [text] that says \"$P<=40: thin Q=140-2P$\"","u6":"a Math [text] that says \"$P=40 thin arrow.r thin pi=1200<1600$\"","uniform_a":"a PlotPoint [gray] labelled \"U_A\" drawn in market (target='demand_curve_a', x=40.0)","uniform_allocation":"a Math [text] that says \"$Q_A=40, quad Q_B=0, quad Q=40$\"","uniform_label":"a Tex [text] that says \"One uniform price\" (underline=True)","uniform_missing_b":"a Polygon [red] drawn in market (vertices=((0.0, 20.0), (0.0, 40.0), (20.0, 20.0)), fill_opacity=0.42)","uniform_price":"a Line [gray] labelled \"P_U=60\" drawn in market (start=(0.0, 60.0), end=(40.0, 60.0), dashed=True)","uniform_total":"a Math [text] that says \"$upright(\"TS\")=2400, quad upright(\"DWL\")=1000$\"","uniform_welfare":"a Math [text] that says \"$upright(\"CS\")=800, quad upright(\"PS\")=1600$\""},"beats":[{"start":440.94006249999995,"say":"Now suppose the seller can separate customers into two observable groups. Group A has stronger demand than group B. The product and marginal cost are the same, but willingness to pay differs.","live":[],"does":[[440.94006249999995,"heading_groups is shown on the screen, written out."],[442.1240625,"restriction is shown on the screen, written out."]]},{"start":453.76556249999993,"say":"This possibility requires strong assumptions. The firm must identify each group, keep customers from pretending to belong to the other group, and prevent low-price buyers from reselling to high-price buyers.","live":["restriction","heading_groups"],"does":[[457.99106249999994,"restriction (the \"identify\" part) is emphasized."],[464.4920625,"restriction (the \"prevent resale\" part) is emphasized."],[466.57056249999994,"restriction (the \"identify\" part) is no longer emphasized."],[466.57056249999994,"restriction (the \"prevent resale\" part) is no longer emphasized."]]},{"start":467.17056249999996,"say":"The blue curve is demand in group A: price equals one hundred minus Q A. The yellow curve is demand in group B: price equals forty minus Q B. The green marginal-cost line is twenty in both markets.","live":null,"does":[[467.68106249999994,"market is shown on the screen, written out."],[467.68106249999994,"demand_curve_a is shown on the screen, drawn."],[472.66206249999993,"demand_curve_b is shown on the screen, drawn."],[477.7130625,"mc_curve is shown on the screen, drawn."]]},{"start":481.85356249999995,"say":"Before allowing separate prices, force the firm to post one common price. That benchmark will show exactly which trades discrimination restores.","live":["restriction","market","heading_groups","demand_curve_a","demand_curve_b","mc_curve"],"does":[[491.14206249999995,"market moves to a new place on the board."],[491.14206249999995,"heading_groups is hidden from the screen — left the board."],[491.14206249999995,"restriction is hidden from the screen — left the board."]]},{"start":492.34206249999994,"say":"At prices of forty or more, group B buys nothing. Only group A remains, with quantity one hundred minus price.","live":["market","demand_curve_a","demand_curve_b","mc_curve"],"does":[[492.34206249999994,"heading_uniform is shown on the screen, written out."],[493.4800625,"u0 is shown on the screen, written out."],[495.48806249999996,"demand_curve_b is indicated — a transient flash."]]},{"start":501.6265625,"say":"Profit is price minus marginal cost, times group A quantity. Differentiate with respect to price. The high-price region has its maximum at a common price of sixty.","live":["market","demand_curve_a","demand_curve_b","mc_curve","u0","heading_uniform"],"does":[[502.03306249999997,"u1 is shown on the screen, written out."],[506.99006249999996,"u2 is shown on the screen, written out."],[512.9340625,"u3 is shown on the screen, written out."]]},{"start":514.3935624999999,"say":"At sixty, group A buys forty units, group B buys none, and profit is sixteen hundred. The gray line and point mark this one-price outcome.","live":["market","demand_curve_a","demand_curve_b","mc_curve","u0","u1","u2","u3","heading_uniform"],"does":[[516.5990625,"u4 is shown on the screen, written out."],[521.6730625,"uniform_price is shown on the screen, written out."],[522.3700624999999,"uniform_a is shown on the screen, written out."]]},{"start":525.2225625,"say":"Could a lower common price that serves both groups do better? Below forty, total quantity is one hundred forty minus two P. Its unconstrained optimum would lie above the permitted range, so the best feasible point in that region is the boundary price forty.","live":["market","demand_curve_a","demand_curve_b","mc_curve","u0","u1","u2","u3","u4","heading_uniform","uniform_price","uniform_a"],"does":[[529.2510625,"u5 is shown on the screen, written out."]]},{"start":542.0645625,"say":"At that boundary profit is only twelve hundred, below sixteen hundred. Therefore the best uniform price is sixty, even though it excludes every buyer in group B.","live":["market","demand_curve_a","demand_curve_b","mc_curve","u0","u1","u2","u3","u4","u5","heading_uniform","uniform_price","uniform_a"],"does":[[544.2590624999999,"u6 is shown on the screen, written out."],[550.4940624999999,"uniform_missing_b is shown on the screen, written out."],[552.7110624999999,"heading_uniform is hidden from the screen — left the board."],[552.7110624999999,"u0 is hidden from the screen — left the board."],[552.7110624999999,"u1 is hidden from the screen — left the board."],[552.7110624999999,"u2 is hidden from the screen — left the board."],[552.7110624999999,"u3 is hidden from the screen — left the board."],[552.7110624999999,"u4 is hidden from the screen — left the board."],[552.7110624999999,"u5 is hidden from the screen — left the board."],[552.7110624999999,"u6 is hidden from the screen — left the board."]]},{"start":553.9110625,"say":"Now allow a separate price in each group. The firm treats each market's marginal revenue independently, while comparing both with the same marginal cost.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","uniform_missing_b"],"does":[[553.9110625,"heading_separate is shown on the screen, written out."],[558.0560624999999,"mr_curve_a is shown on the screen, drawn."],[559.3440625,"mr_curve_b is shown on the screen, drawn."]]},{"start":564.0660624999999,"say":"In group A, marginal revenue equals twenty at quantity forty. Demand then gives price sixty, exactly the outcome group A already had.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","uniform_missing_b","heading_separate","mr_curve_a","mr_curve_b"],"does":[[564.6460625,"separate_work is shown on the screen, written out."],[566.8520625,"separate_work is shown on the screen, written out."],[570.0800624999999,"separate_work is shown on the screen, written out."],[572.6570624999999,"uniform_a is indicated — a transient flash."]]},{"start":574.4645624999999,"say":"In group B, marginal revenue equals twenty at quantity ten. Demand gives a group-B price of thirty, low enough to create ten sales that the uniform price had excluded.","live":null,"does":[[575.1150625,"separate_work is shown on the screen, written out."],[578.0980625,"separate_work is shown on the screen, written out."],[581.8480625,"separate_work is shown on the screen, written out."],[583.5780625,"separate_b is shown on the screen, written out."]]},{"start":586.9415624999999,"say":"Total output rises from forty to fifty, and profit rises from sixteen hundred to seventeen hundred. In this example, segmentation restores trades rather than merely reallocating a fixed total.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","uniform_missing_b","heading_separate","mr_curve_a","mr_curve_b","separate_b"],"does":[[589.0890625,"separate_work is shown on the screen, written out."],[595.8000625,"uniform_missing_b is hidden from the screen."],[596.3340625,"restored_b_cs is shown on the screen, written out."],[596.3340625,"restored_b_ps is shown on the screen, written out."],[596.3340625,"remaining_b_dwl is shown on the screen, written out."],[599.8170625,"heading_separate is hidden from the screen — left the board."],[599.8170625,"separate_work is hidden from the screen — left the board."]]},{"start":600.4170624999999,"say":"Now separate efficiency from distribution. Under one price, forty units are sold, consumer surplus is eight hundred, producer surplus is sixteen hundred, and total surplus is twenty-four hundred.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","mr_curve_a","mr_curve_b","separate_b","restored_b_cs","restored_b_ps","remaining_b_dwl"],"does":[[600.4170624999999,"restored_b_cs is hidden from the screen."],[600.4170624999999,"restored_b_ps is hidden from the screen."],[600.4170624999999,"remaining_b_dwl is hidden from the screen."],[600.4170624999999,"heading_compare is shown on the screen, written out."],[604.0740625,"uniform_label is shown on the screen, written out."],[604.7470625,"uniform_allocation is shown on the screen, written out."],[606.2570625,"uniform_welfare is shown on the screen, written out."],[611.0280625,"uniform_total is shown on the screen, written out."]]},{"start":614.0780625,"say":"The one-price deadweight loss is one thousand. Eight hundred comes from missing group-A trades beyond quantity forty, and two hundred comes from excluding the entire efficient range in group B.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","mr_curve_a","mr_curve_b","separate_b","uniform_label","uniform_allocation","uniform_welfare","uniform_total","heading_compare"],"does":[[616.1100624999999,"uniform_total (the \"upright(\"DWL\")=1000\" part) is indicated — a transient flash."],[619.0130624999999,"remaining_a_dwl is shown on the screen, written out."],[625.3870625,"uniform_missing_b is shown on the screen, written out."]]},{"start":626.9965625,"say":"With two prices, group A remains at forty units while group B gains ten. Total quantity becomes fifty.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","uniform_missing_b","mr_curve_a","mr_curve_b","separate_b","uniform_label","uniform_allocation","uniform_welfare","uniform_total","heading_compare","remaining_a_dwl"],"does":[[627.5890625,"separate_label is shown on the screen, written out."],[631.0950624999999,"uniform_missing_b is hidden from the screen."],[631.0950624999999,"restored_b_cs is shown on the screen, written out."],[631.0950624999999,"restored_b_ps is shown on the screen, written out."],[631.0950624999999,"remaining_b_dwl is shown on the screen, written out."],[633.7070624999999,"separate_allocation is shown on the screen, written out."]]},{"start":635.1665624999999,"say":"The restored group-B trades create one hundred fifty dollars of surplus. Fifty goes to group-B consumers as the yellow triangle, and one hundred goes to the firm as the magenta rectangle.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","mr_curve_a","mr_curve_b","separate_b","restored_b_cs","restored_b_ps","remaining_b_dwl","uniform_label","uniform_allocation","uniform_welfare","uniform_total","separate_label","separate_allocation","heading_compare","remaining_a_dwl"],"does":[[637.2910625,"restored_b_ps is indicated — a transient flash."],[637.7900625,"restored_b_cs is indicated — a transient flash."]]},{"start":647.0050625,"say":"Consumer surplus across both groups rises to eight hundred fifty, producer surplus rises to seventeen hundred, and total surplus rises to twenty-five hundred fifty.","live":null,"does":[[647.3530625,"separate_welfare is shown on the screen, written out."],[654.0170625,"separate_total is shown on the screen, written out."]]},{"start":657.6475625,"say":"Deadweight loss falls from one thousand to eight hundred fifty. It does not disappear: group A still stops at forty, and group B still stops at ten instead of the efficient quantity twenty.","live":["market","demand_curve_a","demand_curve_b","mc_curve","uniform_price","uniform_a","mr_curve_a","mr_curve_b","separate_b","restored_b_cs","restored_b_ps","remaining_b_dwl","uniform_label","uniform_allocation","uniform_welfare","uniform_total","separate_label","separate_allocation","separate_welfare","separate_total","heading_compare","remaining_a_dwl"],"does":[[660.3870625,"separate_total (the \"upright(\"DWL\")=850\" part) is indicated — a transient flash."],[664.0210625,"remaining_a_dwl is indicated — a transient flash."],[666.3900624999999,"remaining_b_dwl is indicated — a transient flash."]]},{"start":670.8675625,"say":"This welfare improvement is an example, not a universal theorem. Third-degree discrimination can raise or lower total output, and it can redirect units toward groups with higher or lower willingness to pay.","live":null,"does":[]},{"start":684.2735625,"say":"What is reliable is the firm's incentive: if separation is voluntary and feasible, its profit rises. What happens to total surplus depends on which trades appear, which disappear, and how production is reallocated. Who captures the gains is a further question, distinct from whether gains exist at all.","live":null,"does":[[690.7170625,"separate_welfare (the \"upright(\"PS\")=1700\" part) is emphasized."],[693.4220624999999,"separate_welfare (the \"upright(\"PS\")=1700\" part) is no longer emphasized."],[704.695375,"heading_compare is hidden from the screen — left the board."],[704.695375,"market is hidden from the screen — left the board."],[704.695375,"demand_curve_a is hidden from the screen — market left the board."],[704.695375,"demand_curve_b is hidden from the screen — market left the board."],[704.695375,"mc_curve is hidden from the screen — market left the board."],[704.695375,"uniform_price is hidden from the screen — market left the board."],[704.695375,"uniform_a is hidden from the screen — market left the board."],[704.695375,"mr_curve_a is hidden from the screen — market left the board."],[704.695375,"mr_curve_b is hidden from the screen — market left the 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the board."]]}]},{"title":"Perfect Discrimination and the Whole Surplus","start":705.7370416666668,"end":936.2115625000001,"objects":{"assumption":"a Panel that says \"The firm knows each buyer's exact willingness to pay, can charge each unit that amount, prevents resale, and faces constant marginal cost 20.\"","buyer":"a PlotPoint [yellow] labelled \"5\" drawn in plot (target='demand_curve', x=<VariableNumber unit = 39.5>)","demand_curve":"a FunctionPlot [blue] labelled \"D\" drawn in plot (function=<function>, x_range=(0.0, 50.0))","efficient_point":"a PlotPoint [green] labelled \"E\" drawn in plot (target='demand_curve', x=40.0)","efficient_quantity":"a Line [green] drawn in plot (start=(40.0, 0.0), end=(40.0, 20.0), dashed=True)","heading_compare":"a Heading that says \"Efficiency Returns, Distribution Changes\"","heading_rule":"a Heading that says \"Produce Every Unit Worth Its Cost\"","heading_units":"a Heading that says \"A Different Price for Every Unit\"","mc_curve":"a 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P=30$\"","price_40":"a Math [text] that says \"$Q=40 thin arrow.r thin P=20$\"","price_5":"a Math [text] that says \"$Q=5 thin arrow.r thin P=90$\"","unit":"a VariableNumber (initial_value=5.0, format_spec='.0f')","unit_surplus":"a Line [magenta] drawn in plot (start=(<VariableNumber unit = 39.5>, 20.0), end=(<VariableNumber unit = 39.5>, (100.0 - (2.0 * unit))))"},"beats":[{"start":705.7370416666668,"say":"Perfect, or first-degree, price discrimination is a much stronger benchmark. The firm knows each buyer's exact willingness to pay and can charge that amount unit by unit.","live":[],"does":[[705.7370416666668,"heading_units is shown on the screen, written out."],[705.7950416666667,"assumption is shown on the screen, written out."]]},{"start":717.1230416666667,"say":"It must also prevent resale. Otherwise a buyer offered a low price could resell to someone facing a high price, and the entire pricing scheme would unravel.","live":["assumption","heading_units"],"does":[[718.1440416666668,"assumption (the \"prevents resale\" part) is emphasized."],[727.3160416666667,"assumption (the \"prevents resale\" part) is no longer emphasized."]]},{"start":727.9160416666667,"say":"The blue demand curve now has a second interpretation. Its height at each quantity is the willingness to pay for that marginal unit. The green line remains marginal cost twenty.","live":null,"does":[[728.5540416666668,"plot is shown on the screen, written out."],[728.5540416666668,"demand_curve is shown on the screen, drawn."],[736.8440416666667,"mc_curve is shown on the screen, drawn."]]},{"start":740.9585416666667,"say":"Begin near the left. The fifth unit is worth ninety dollars to its buyer. Under perfect discrimination, the firm can charge ninety for that unit without lowering the prices paid for the units before it.","live":["assumption","plot","heading_units","demand_curve","mc_curve"],"does":[[740.9585416666667,"assumption is hidden from the screen — left the board."],[740.9585416666667,"price_5 is shown on the screen, written out."],[743.3150416666667,"buyer is shown on the screen, written out."],[743.3150416666667,"unit_surplus is shown on the screen, written out."]]},{"start":753.9690416666667,"say":"That last clause removes the price-cut loss that pushed marginal revenue below demand under one-price monopoly. Each unit contributes its own willingness to pay, less its own production cost.","live":["plot","heading_units","demand_curve","mc_curve","price_5","buyer","unit_surplus"],"does":[[761.9450416666667,"unit_surplus is indicated — a transient flash."]]},{"start":767.0845416666667,"say":"Move to unit twenty. Its willingness to pay is sixty. Earlier buyers may still pay more than sixty because their individual prices do not have to match this buyer's price.","live":null,"does":[[768.0590416666668,"buyer is redrawn as the numbers it depends on change."],[768.0590416666668,"unit_surplus is redrawn as the numbers it depends on change."],[768.0590416666668,"unit ticks to 20.0."],[770.4740416666667,"price_20 is shown on the screen, written out."]]},{"start":778.6320416666667,"say":"Move farther, to unit thirty-five. That buyer is willing to pay thirty, still ten dollars above marginal cost, so producing the unit creates ten dollars of total surplus.","live":["plot","heading_units","demand_curve","mc_curve","price_5","price_20","buyer","unit_surplus"],"does":[[780.3160416666667,"buyer is redrawn as the numbers it depends on change."],[780.3160416666667,"unit_surplus is redrawn as the numbers it depends on change."],[780.3160416666667,"unit ticks to 35.0."],[782.9510416666667,"price_35 is shown on the screen, written out."],[783.9610416666668,"unit_surplus is indicated — a transient flash."]]},{"start":789.8670416666668,"say":"Approach unit forty. At unit forty, willingness to pay is twenty, exactly marginal cost. Beyond forty, willingness to pay would be below cost, so those units should not be produced.","live":["plot","heading_units","demand_curve","mc_curve","price_5","price_20","price_35","buyer","unit_surplus"],"does":[[790.1690416666668,"buyer is redrawn as the numbers it depends on change."],[790.1690416666668,"unit_surplus is redrawn as the numbers it depends on change."],[790.1690416666668,"unit ticks to 39.5."],[791.1090416666667,"point is shown on the screen, grown."],[793.1090416666667,"point is hidden from the screen."],[794.8710416666668,"price_40 is shown on the screen, written out."]]},{"start":803.8125416666668,"say":"The rule is now different from one-price monopoly. Revenue from the marginal unit equals that unit's own demand price because selling it does not reduce the prices charged on earlier units.","live":["plot","heading_units","demand_curve","mc_curve","price_5","price_20","price_35","price_40","buyer","unit_surplus"],"does":[[803.8125416666668,"plot moves to a new place on the board."],[803.8125416666668,"heading_units is hidden from the screen — left the board."],[803.8125416666668,"price_20 is hidden from the screen — left the board."],[803.8125416666668,"price_35 is hidden from the screen — left the board."],[803.8125416666668,"price_40 is hidden from the screen — left the board."],[803.8125416666668,"price_5 is hidden from the screen — left the board."],[803.8125416666668,"heading_rule is shown on the screen, written out."],[803.8125416666668,"perfect_work is shown on the screen, written out."]]},{"start":816.1090416666667,"say":"Produce while willingness to pay is at least marginal cost. For our market, set one hundred minus two Q equal to twenty.","live":["plot","demand_curve","mc_curve","buyer","unit_surplus","heading_rule"],"does":[[816.4570416666668,"perfect_work is shown on the screen, written out."],[822.1120416666668,"perfect_work is shown on the screen, written out."]]},{"start":826.3225416666668,"say":"The result is quantity forty, the same efficient quantity produced under competition. Perfect discrimination restores every trade whose value covers its cost.","live":null,"does":[[827.9590416666667,"perfect_work is shown on the screen, written out."],[829.2360416666668,"efficient_quantity is shown on the screen, written out."],[830.6990416666667,"efficient_point is shown on the screen, written out."]]},{"start":837.5105416666668,"say":"Efficiency has returned, but competitive pricing has not. There is no one price here. Early units carry high prices, later units carry lower prices, and the final unit is priced at marginal cost.","live":["plot","demand_curve","mc_curve","buyer","unit_surplus","heading_rule","efficient_quantity","efficient_point"],"does":[[837.8590416666667,"A box is drawn around perfect_work."]]},{"start":852.4220416666667,"say":"Return briefly to the one-price monopoly. It sold twenty units at sixty. 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The missing red trades return, so deadweight loss falls from four hundred to zero.","live":["plot","demand_curve","mc_curve","buyer","unit_surplus","efficient_quantity","efficient_point","one_price_label","one_price_allocation","one_price_surplus","one_price_total","heading_compare","monopoly_quantity","monopoly_point","monopoly_cs","monopoly_ps","monopoly_dwl"],"does":[[866.2230416666667,"monopoly_cs is hidden from the screen."],[866.2230416666667,"monopoly_ps is hidden from the screen."],[866.8380416666666,"perfect_label is shown on the screen, written out."],[869.8100416666667,"perfect_allocation is shown on the screen, written out."],[869.8100416666667,"efficient_quantity is indicated — a transient flash."],[872.1560416666667,"monopoly_dwl is hidden from the screen."]]},{"start":876.5290416666667,"say":"But each buyer is charged exactly what the unit is worth to that buyer. The difference between willingness to pay and marginal cost is therefore captured by the firm, not left with consumers.","live":["plot","demand_curve","mc_curve","buyer","unit_surplus","efficient_quantity","efficient_point","one_price_label","one_price_allocation","one_price_surplus","one_price_total","perfect_label","perfect_allocation","heading_compare","monopoly_quantity","monopoly_point"],"does":[[884.9580416666668,"perfect_ps is shown on the screen, written out."]]},{"start":888.6345416666668,"say":"Producer surplus becomes the entire magenta triangle, sixteen hundred. Consumer surplus is zero because every buyer pays their full willingness to pay.","live":["plot","demand_curve","mc_curve","buyer","unit_surplus","efficient_quantity","efficient_point","one_price_label","one_price_allocation","one_price_surplus","one_price_total","perfect_label","perfect_allocation","heading_compare","monopoly_quantity","monopoly_point","perfect_ps"],"does":[[891.0030416666667,"perfect_ps is indicated — a transient flash."],[892.3850416666667,"perfect_surplus_line is shown on the screen, written out."]]},{"start":899.6140416666667,"say":"Total surplus is also sixteen hundred, the same efficient total as under competition. The firm has not created extra value beyond the efficient allocation. It has changed who receives that value.","live":["plot","demand_curve","mc_curve","buyer","unit_surplus","efficient_quantity","efficient_point","one_price_label","one_price_allocation","one_price_surplus","one_price_total","perfect_label","perfect_allocation","perfect_surplus_line","heading_compare","monopoly_quantity","monopoly_point","perfect_ps"],"does":[[899.9160416666667,"perfect_total is shown on the screen, written out."],[901.2630416666667,"perfect_total (the \"upright(\"TS\")=1600\" part) is emphasized."],[911.0740416666667,"perfect_total (the \"upright(\"TS\")=1600\" part) is no longer emphasized."]]},{"start":913.4155416666667,"say":"That completes the distinction. A one-price monopolist restricts quantity because expanding sales lowers the price on earlier units. Third-degree discrimination may restore some trades by separating groups. Perfect discrimination restores every efficient trade, eliminates deadweight loss, and transfers the available surplus to the monopolist.","live":["plot","demand_curve","mc_curve","buyer","unit_surplus","efficient_quantity","efficient_point","one_price_label","one_price_allocation","one_price_surplus","one_price_total","perfect_label","perfect_allocation","perfect_surplus_line","perfect_total","heading_compare","monopoly_quantity","monopoly_point","perfect_ps"],"does":[[917.3980416666667,"one_price_total (the \"upright(\"DWL\")=400\" part) is indicated — a transient flash."],[930.2150416666667,"perfect_total (the \"upright(\"DWL\")=0\" part) is indicated — a transient flash."],[935.1698958333334,"heading_compare is hidden from the screen — left the board."],[935.1698958333334,"one_price_allocation is hidden from the screen — left the board."],[935.1698958333334,"one_price_label is hidden from the screen — left the board."],[935.1698958333334,"one_price_surplus is hidden from the screen — left the board."],[935.1698958333334,"one_price_total is hidden from the screen — left the board."],[935.1698958333334,"perfect_allocation is hidden from the screen — left the board."],[935.1698958333334,"perfect_label is hidden from the screen — left the board."],[935.1698958333334,"perfect_surplus_line is hidden from the screen — left the board."],[935.1698958333334,"perfect_total is hidden from the screen — left the board."],[935.1698958333334,"plot is hidden from the screen — left the board."],[935.1698958333334,"demand_curve is hidden from the screen — plot left the board."],[935.1698958333334,"mc_curve is hidden from the screen — plot left the board."],[935.1698958333334,"buyer is hidden from the screen — plot left the board."],[935.1698958333334,"unit_surplus is hidden from the screen — plot left the board."],[935.1698958333334,"efficient_quantity is hidden from the screen — plot left the board."],[935.1698958333334,"efficient_point is hidden from the screen — plot left the board."],[935.1698958333334,"monopoly_quantity is hidden from the screen — plot left the board."],[935.1698958333334,"monopoly_point is hidden from the screen — plot left the board."],[935.1698958333334,"perfect_ps is hidden from the screen — plot left the board."]]}]}]},"durationSeconds":936,"chapters":[{"title":"One More Unit Changes Every Price","startSeconds":0,"narration":"A monopolist is the only seller, but that does not make demand disappear. Buyers still decide how many units they will purchase at each price. The firm may choose a point on market demand, not a price and quantity independently. Here is a market demand curve. Quantity runs across the bottom, price runs up the side, and the downward slope says that reaching more buyers requires a lower price. At quantity twenty, demand allows a price of sixty. The point twenty, sixty is therefore one feasible price-quantity choice, and the rectangle beneath it is the firm's total revenue. Read that choice algebraically. Demand gives sixty dollars per unit, and twenty units at sixty dollars produce total revenue of twelve hundred dollars. Now ask the firm to sell one additional unit. Demand says quantity twenty-one can be sold only if the market price falls from sixty to fifty-eight. The extra unit brings in fifty-eight dollars. That is the narrow green strip. But the firm must also cut the price by two dollars on each of the twenty units it was already selling. The red band is that lost revenue: twenty earlier units times a two-dollar reduction, or forty dollars lost. Marginal revenue is the green gain minus the red loss, not simply the new unit's price. Fifty-eight gained minus forty lost leaves only eighteen dollars of additional revenue. The new unit sells for fifty-eight, yet its marginal revenue is eighteen. That gap between price and marginal revenue is the central monopoly constraint. Expanding sales earns revenue on the new unit, but lowering one market price sacrifices revenue on every earlier unit. The same logic can be written for every quantity on a linear demand curve. Let inverse demand be price equals a minus b Q. The intercept a is the price of the first infinitesimal unit. The coefficient b records how quickly the market price must fall as total output rises. Total revenue is price times quantity. Substitute demand into that product, then multiply out. Revenue is a Q minus b Q squared. Differentiate revenue with respect to quantity. The derivative of a Q is a, while the derivative of minus b Q squared is minus two b Q. So marginal revenue has the same vertical intercept a as demand, but its slope is minus two b instead of minus b. It falls twice as fast because the price reduction applies to the old units as well as the new one. For our numerical demand, price is one hundred minus two Q. Marginal revenue is one hundred minus four Q. Draw the red marginal-revenue curve. Both curves begin at one hundred. Demand reaches the quantity axis at fifty, while marginal revenue reaches it halfway across, at twenty-five. The algebra and the graph tell the same story. Linear demand falls by two dollars per additional unit; marginal revenue falls by four because it includes both the new sale and the price cut imposed on existing sales."},{"title":"The Monopoly Choice and the Missing Trades","startSeconds":210.46554166666664,"narration":"Now turn marginal revenue into a quantity decision. We will keep one posted price, constant marginal cost of twenty, and no fixed cost. Those assumptions make the allocation and the welfare accounting transparent. The blue curve is demand, the red curve is marginal revenue, and the green line is marginal cost. Demand describes buyers. Marginal revenue and marginal cost describe the consequence of producing one more unit. At quantity ten, marginal revenue exceeds marginal cost. Another unit adds more to revenue than to cost, so stopping there would leave profitable units unproduced. Push output to twenty-five. Marginal revenue has fallen below marginal cost, so the last units destroy profit. Move back until the red and green readings meet, at quantity twenty. The interior profit maximum therefore satisfies marginal revenue equal to marginal cost. Substitute the numerical curves: one hundred minus four Q equals twenty. Solving gives the monopoly quantity, twenty. Notice what has been chosen so far: quantity, not price. To find the price, move vertically from quantity twenty to the demand curve. Demand says buyers will pay sixty for each of those twenty units. This order matters. Marginal revenue equal to marginal cost selects quantity. Demand then supplies the single market price. Reading price from marginal revenue would confuse an incremental revenue with what buyers actually pay. For the competitive benchmark, price equals marginal cost. Demand reaches twenty dollars at quantity forty, so competition produces forty units at a price of twenty. Place the two outcomes beside the same market. Monopoly stops at twenty and charges sixty. Competition continues to forty and charges twenty. Under monopoly, the yellow triangle is consumer surplus. Buyers receive the difference between willingness to pay and the sixty-dollar price on the twenty units sold. The magenta rectangle is producer surplus. With constant marginal cost twenty and price sixty, the firm receives forty dollars of surplus on each of twenty units, for eight hundred. The red triangle contains quantities twenty through forty. For every unit there, willingness to pay exceeds marginal cost, yet the monopolist does not sell it because expansion would force down the price on earlier units. Those are mutually beneficial trades that never occur. Their lost total surplus is deadweight loss, four hundred. Monopoly total surplus is twelve hundred. Switch to competition. Output reaches forty, the point where willingness to pay just equals marginal cost. The formerly missing trades now occur. With price equal to constant marginal cost and no fixed cost, consumer surplus is sixteen hundred and producer surplus is zero. Total surplus is sixteen hundred, and deadweight loss is zero. The competitive benchmark maximizes total surplus because every unit worth at least its cost is produced. The monopoly restriction lowers quantity from forty to twenty and destroys four hundred of that possible value. Two questions must remain separate. Efficiency asks how much total value is created. Distribution asks whether buyers or the firm capture that value. Monopoly changes both, but the missing red triangle is a loss to everyone, not a transfer between them."},{"title":"Two Groups, Two Prices","startSeconds":440.94006249999995,"narration":"Now suppose the seller can separate customers into two observable groups. Group A has stronger demand than group B. The product and marginal cost are the same, but willingness to pay differs. This possibility requires strong assumptions. The firm must identify each group, keep customers from pretending to belong to the other group, and prevent low-price buyers from reselling to high-price buyers. The blue curve is demand in group A: price equals one hundred minus Q A. The yellow curve is demand in group B: price equals forty minus Q B. The green marginal-cost line is twenty in both markets. Before allowing separate prices, force the firm to post one common price. That benchmark will show exactly which trades discrimination restores. At prices of forty or more, group B buys nothing. Only group A remains, with quantity one hundred minus price. Profit is price minus marginal cost, times group A quantity. Differentiate with respect to price. The high-price region has its maximum at a common price of sixty. At sixty, group A buys forty units, group B buys none, and profit is sixteen hundred. The gray line and point mark this one-price outcome. Could a lower common price that serves both groups do better? Below forty, total quantity is one hundred forty minus two P. Its unconstrained optimum would lie above the permitted range, so the best feasible point in that region is the boundary price forty. At that boundary profit is only twelve hundred, below sixteen hundred. Therefore the best uniform price is sixty, even though it excludes every buyer in group B. Now allow a separate price in each group. The firm treats each market's marginal revenue independently, while comparing both with the same marginal cost. In group A, marginal revenue equals twenty at quantity forty. Demand then gives price sixty, exactly the outcome group A already had. In group B, marginal revenue equals twenty at quantity ten. Demand gives a group-B price of thirty, low enough to create ten sales that the uniform price had excluded. Total output rises from forty to fifty, and profit rises from sixteen hundred to seventeen hundred. In this example, segmentation restores trades rather than merely reallocating a fixed total. Now separate efficiency from distribution. Under one price, forty units are sold, consumer surplus is eight hundred, producer surplus is sixteen hundred, and total surplus is twenty-four hundred. The one-price deadweight loss is one thousand. Eight hundred comes from missing group-A trades beyond quantity forty, and two hundred comes from excluding the entire efficient range in group B. With two prices, group A remains at forty units while group B gains ten. Total quantity becomes fifty. The restored group-B trades create one hundred fifty dollars of surplus. Fifty goes to group-B consumers as the yellow triangle, and one hundred goes to the firm as the magenta rectangle. Consumer surplus across both groups rises to eight hundred fifty, producer surplus rises to seventeen hundred, and total surplus rises to twenty-five hundred fifty. Deadweight loss falls from one thousand to eight hundred fifty. It does not disappear: group A still stops at forty, and group B still stops at ten instead of the efficient quantity twenty. This welfare improvement is an example, not a universal theorem. Third-degree discrimination can raise or lower total output, and it can redirect units toward groups with higher or lower willingness to pay. What is reliable is the firm's incentive: if separation is voluntary and feasible, its profit rises. What happens to total surplus depends on which trades appear, which disappear, and how production is reallocated. Who captures the gains is a further question, distinct from whether gains exist at all."},{"title":"Perfect Discrimination and the Whole Surplus","startSeconds":705.7370416666668,"narration":"Perfect, or first-degree, price discrimination is a much stronger benchmark. The firm knows each buyer's exact willingness to pay and can charge that amount unit by unit. It must also prevent resale. Otherwise a buyer offered a low price could resell to someone facing a high price, and the entire pricing scheme would unravel. The blue demand curve now has a second interpretation. Its height at each quantity is the willingness to pay for that marginal unit. The green line remains marginal cost twenty. Begin near the left. The fifth unit is worth ninety dollars to its buyer. Under perfect discrimination, the firm can charge ninety for that unit without lowering the prices paid for the units before it. That last clause removes the price-cut loss that pushed marginal revenue below demand under one-price monopoly. Each unit contributes its own willingness to pay, less its own production cost. Move to unit twenty. Its willingness to pay is sixty. Earlier buyers may still pay more than sixty because their individual prices do not have to match this buyer's price. Move farther, to unit thirty-five. That buyer is willing to pay thirty, still ten dollars above marginal cost, so producing the unit creates ten dollars of total surplus. Approach unit forty. At unit forty, willingness to pay is twenty, exactly marginal cost. Beyond forty, willingness to pay would be below cost, so those units should not be produced. The rule is now different from one-price monopoly. Revenue from the marginal unit equals that unit's own demand price because selling it does not reduce the prices charged on earlier units. Produce while willingness to pay is at least marginal cost. For our market, set one hundred minus two Q equal to twenty. The result is quantity forty, the same efficient quantity produced under competition. Perfect discrimination restores every trade whose value covers its cost. Efficiency has returned, but competitive pricing has not. There is no one price here. Early units carry high prices, later units carry lower prices, and the final unit is priced at marginal cost. Return briefly to the one-price monopoly. It sold twenty units at sixty. The yellow triangle was consumer surplus, the magenta rectangle was producer surplus, and the red triangle was deadweight loss. Under perfect discrimination, output extends from twenty to forty. The missing red trades return, so deadweight loss falls from four hundred to zero. But each buyer is charged exactly what the unit is worth to that buyer. The difference between willingness to pay and marginal cost is therefore captured by the firm, not left with consumers. Producer surplus becomes the entire magenta triangle, sixteen hundred. Consumer surplus is zero because every buyer pays their full willingness to pay. Total surplus is also sixteen hundred, the same efficient total as under competition. The firm has not created extra value beyond the efficient allocation. It has changed who receives that value. That completes the distinction. A one-price monopolist restricts quantity because expanding sales lowers the price on earlier units. Third-degree discrimination may restore some trades by separating groups. Perfect discrimination restores every efficient trade, eliminates deadweight loss, and transfers the available surplus to the monopolist."}]}}